use the discriminant to describe the roots of each equation x^2+2x+5=0

Answer 1

The discriminant b^2-4ac is the part of the quadratic formula under the square root sign so if b^-4ac is negative then part of the root will contain the square root of a negative number. There is no real number which satisfies this so the roots are imaginary

In this case b^2 -4ac = (2)^2 - (4x5x1)= 4-20 = -16

Since the discriminant is negative the roots are therefore imaginary

Answer 2

Hello Erin!

The discriminant of the equation is:

Δ = 2² - 4*1*5 = 4 - 20 = -16

The roots of the equation are imaginary, because the discriminant is below zero